Number of Local Minimums

[Puzzle Prime]

100 real random numbers between 0 and 1 are written in a row. What is the expected number of local minima in the row, i.e. numbers which do not stand next to a smaller number?

[Vivek]

Using Indicator variables. And the ending point situations have probability of 1/2 to be local minimum and others have 1/6. So, 2*(1/2)+98*(1/6) =52/3 =17.3333 ?

[Puzzle Prime]

Yes, this approach works here too 🙂

[Vivek]

Oops made a mistake…it is 1/3 right? Not 1/6.

[Puzzle Prime]

Yeah it is, 213 and 312. Sorry didn’t notice 🙂